﻿ 浅水中海洋核动力平台低频响应分析
 舰船科学技术  2019, Vol. 41 Issue (10): 124-128 PDF

1. 武汉第二船舶设计研究所，湖北 武汉 430064;
2. 太原（天津）重型机械有限公司，天津 300450

Analysis on low frequency response of marine nuclear power platform in shallow water
LIANG Shuang-ling1, GUO Xin-jie2
1. Wuhan Second Ship Design and Research Institute, Wuhan 430064, China;
2. Taiyuan (Tianjin) Heavy Machinery Group Company, Tianjin 300450, China
Abstract: Unlike wave spectrums derived from the theoretical formula, the wave spectrums in real shallow water contain obvious low frequency energy part in frequency range of 0～0.2 rad/s, which would play a great influence on the LF response of marine nuclear power platform. Thus, based on the wave spectrums get from numerical simulation and basin test two methods, surge, heave and pitch LF responses in two different wave spectrums are analyzed adopting numerical calculation in frequency domain. Results shows that compared with the wave spectrums from numerical simulation, first order LF motion response and second order LF wave drift force in surge direction, first order LF wave force and first order LF motion response in heave direction all increase obviously in the real wave spectrums from basin tank, which means that it should pay more attention to the effect of LF energy part on the low frequency response of platform in the process of hydrodynamic prediction in shallow water. This paper can provide a helpful reference for the same type ships when proceeding the LF response prediction in shallow water.
Key words: shallow water     marine nuclear power platform     low frequency response     wave loads     motion response
0 引　言

1 理论基础 1.1 纵荡运动方程

 $\begin{split}& \left[ {m + {a_{11}}\left( {{\mu _1}} \right)} \right]{\ddot x_{1L}} + \left[ {{B_{11}}\left( {{\mu _1}} \right) + {B_{wdd}}} \right]{\dot x_{1L}} + \\ &\quad\quad{C_{11}}{x_{1L}} = {F_{1L}}\text{。}\end{split}$ (1)

 ${S_{{x_{1L}}}}\left( \mu \right) = \frac{{{S_{{F_{1L}}}}\left( \mu \right)}}{{{{\left[ {{C_{11}} - \left( {m + {a_{11}}} \right){\mu ^2}} \right]}^2} + {{\left( {{B_{11}} + {B_{wdd}}} \right)}^2}{\mu ^2}}}\text{。}$ (2)

 $\sigma _{{x_{1L}}}^2 = \int_0^\infty {{S_{{x_{1L}}}}\left( \mu \right)} {\rm{d}}\mu = \frac{{\text{π}} }{{2\left( {{B_{11}} + {B_{wdd}}} \right){C_{11}}}}{S_{{F_{1L}}}}\left( {{\mu _1}} \right)\text{。}$ (3)

 $S_{{F_{1L}}}^{\left( 1 \right)}\left( \omega \right) = S\left( \omega \right){\left| {{H_{{F_{1L}}}}\left( \omega \right)} \right|^2}\text{，}$ (4)

2阶平均波浪力决定了平台的平均位移，可以表示为：

 $F_{1L}^{\left( 2 \right)} = 2\int_0^\infty {S\left( \omega \right)T\left( {\omega ,\omega } \right)} {\rm{d}}\omega \text{，}$ (5)

2阶波浪慢漂力谱密度函数可以表示为：

 $S_{{F_{1L}}}^{\left( 2 \right)}\left( \mu \right) = 8\int_0^\infty {S\left( {\omega + \mu } \right)S\left( \omega \right){T^2}\left( {\omega + \mu ,\omega } \right){\rm{d}}\omega }\text{，}$ (6)

 ${S_{{F_{1L}}}}\left( \mu \right) = S_{{F_{1L}}}^{(1)}\left( \mu \right) + S_{{F_{1L}}}^{(2)}\left( \mu \right)\text{，}$ (7)

 ${B_{11}}\left( {{\mu _1}} \right) = 2\delta \sqrt {{C_{11}}\left[ {m + {a_{11}}\left( {{\mu _1}} \right)} \right]} = \frac{{2\delta {C_{11}}}}{{{\mu _1}}}\text{，}$ (8)

 $\delta = \frac{{\ln {x_1} - \ln {x_{n + 1}}}}{{2{\text{π}} n}}\text{。}$ (9)

 ${B_{wdd}} = 2\int_0^\infty {S\left( \omega \right){b_{wdd}}\left( \omega \right){\rm{d}}\omega } \text{，}$ (10)
 ${b_{wdd}}\left( \omega \right) = - \frac{\omega }{g}\left[ {\omega \frac{{{\rm{d}}T\left( {\omega ,\omega } \right)}}{{{\rm{d}}\omega }} + 4T\left( {\omega ,\omega } \right)} \right]\text{。}$ (11)
1.2 垂荡和纵摇运动方程

 $\begin{split}\!\!\!\!\!\! \sum\limits_{j = 1}^6 {\left\{ {\left[ {{m_{ij}} + {a_{ij}}\left( \omega \right)} \right]\ddot x_j^{\left( 1 \right)} + {\lambda _{ij}}\left( \omega \right)\dot x_j^{\left( 1 \right)} + {C_{ij}}x_j^{\left( 1 \right)}} \right\}} = F_i^{\left( 1 \right)}\text{，} \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;i = 3,5\text{。} \end{split}$ (12)

 $\sigma _{{x_{iL}}}^2 = \int_0^\infty {{S_{{x_{iL}}}}\left( \omega \right)} {\rm{d}}\omega\text{，} \;\;i = 3,5\text{。}$ (13)
2 海洋核动力平台

 图 1 船体网格划分示意图 Fig. 1 Sketch of ship meshing

 图 2 软刚臂系泊系统总体布置 Fig. 2 General arrangement of soft yoke mooring system

 图 3 单点系泊系统纵荡水平回复力曲线 Fig. 3 Horizontal restoring force of soft yoke mooring system in surge direction
3 数值计算结果与比较分析 3.1 不规则波校验

 图 4 波浪谱密度计算值与试验值对比结果 Fig. 4 Comparative results of calculating and experimental wave spectrums

3.2 纵荡低频响应

 图 5 纵荡1阶低频波浪力谱 Fig. 5 First order LF wave force spectrum in surge direction

 图 7 纵荡2阶波浪慢漂力 Fig. 7 Second order wave slow drift force in surge direction

 图 8 纵荡低频波浪力标准差对比 Fig. 8 Standard deviation comparison of LF wave force in surge direction

 图 6 纵荡2阶平均波浪力 Fig. 6 Second order mean wave force in surge direction

2）由图8可知，浅水低频能量成分对纵荡1阶低频波浪力、2阶平均波浪力影响较小，而对2阶波浪慢漂力影响很大，考虑浅水低频能量成分相比于不考虑时2阶波浪慢漂力增大1倍左右。

 ${\mu _1} = \sqrt {{{{C_{11}}} / {\left[ {m + {a_{11}}\left( \infty \right)} \right]}}} \text{。}$ (14)

 图 9 纵荡运动标准差对比 Fig. 9 Standard deviation comparison of motion response in surge direction
3.3 垂荡和纵摇低频响应

 图 10 垂荡1阶低频波浪力谱 Fig. 10 First order LF wave force spectrum in heave direction

 图 11 纵摇1阶低频波浪力谱 Fig. 11 First order LF wave force spectrum in pitch direction

 图 12 垂荡1阶低频运动响应谱 Fig. 12 First order LF motion response spectrum in heave direction

 图 13 纵摇1阶低频运动响应谱 Fig. 13 First order LF motion response spectrum in pitch direction

 图 14 垂荡和纵摇1阶低频响应标准差对比 Fig. 14 Standard deviation comparison of first order LF response in heave and pitch direction

1）由图10图12可知，浅水波浪谱中的低频能量成分对垂荡1阶低频波浪力和1阶低频运动响应的影响非常大；

2）由图14可知，浅水低频能量成分使得垂荡1阶波浪力增大1倍左右，相应地使得垂荡1阶运动响应增大38.2%，而对纵摇低频波浪力和低频运动响应影响较小。

4 结　语

1）浅水中的低频能量成分在通常数值计算中所应用的不规则波理论中是不存在的，由于其对平台的低频波浪力和低频运动响应十分重要，在理论预报时必须予以特别重视；

2）浅水低频能量成分对平台纵荡2阶波浪慢漂力和纵荡1阶低频运动响应影响很大；

3）浅水低频能量成分使得垂荡1阶低频波浪力和1阶低频运动响应出现了非常大的能量成分，说明其对垂荡低频响应影响很大。

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